Predictive regression with order-p autoregressive predictors

Studies of predictive regressions analyze the case where yt is predicted by xt − 1 with xt being first-order autoregressive, AR(1). Under some conditions, the OLS-estimated predictive coefficient is known to be biased. We analyze a predictive model where yt is predicted by xt − 1, xt − 2,… xt − p with xt being autoregressive of order p, AR(p) with p > 1. We develop a generalized augmented regression method that produces a reduced-bias point estimate of the predictive coefficients and derive an appropriate hypothesis testing procedure. We apply our method to the prediction of quarterly stock returns by dividend yield, which is apparently AR(2). Using our method results in the AR(2) predictor series having insignificant effect, although under OLS, or the commonly assumed AR(1) structure, the predictive model is significant. We also generalize our method to the case of multiple AR(p) predictors.